Approximation by Truncated Lupas Operators of Max-Product Kind

Abstract

The goals of the present paper are to introduce truncated Lupas type operators of max-product kind and give an estimation for the degree of approximation with respect to first modulus of continuity function. We prove that this estimate can not be improved; on the other hand, for some subclasses of functions, better degree of approximation is obtained. We also showed the piecewise convexity of the constructed operators on the interval [0, 1].